1. Field of the Invention
The present invention relates to a gas analyzer for measuring a molecular number density of a component to be measured in a sample gas by means of absorption of laser gas.
2. Description of the Related Art
In recent years, as a method for measuring a molecular number density of a specific gas in a vapor, laser absorption spectroscopy by means of absorption of laser light has been proposed (e.g., Unexamined Japanese Patent Publication No. 5-099845). This method is to irradiate a sample cell, where a sample gas has been introduced, with laser light with a predetermined frequency and to analyze the transmitted laser light, to derive a molecular number density of a component to be measured in the sample gas from the degree of absorption in the component to be measured. This device is a non-contact type where a light receiving section as a sensor is not in contact with the sample gas, thereby having an advantage of being capable of measurement without disturbing a sample place and an advantage of having extremely short response time. In order to select a measurement frequency with respect to the component to be measured in the sample gas, a wavelength tunable laser is used as a light source of laser light.
Hereinafter, a general theory of infrared absorption spectroscopy using laser light will be described. It is to be noted that the case of measuring minute amounts of water-vapor molecular number densities in a nitrogen gas will here be taken as an example.
The relation between a detected light reception intensity of laser light and a water-vapor molecular number density is shown by Formula (1) from the following Lambert-Beer Law. I0(ν) is a light intensity in the case of light without absorption by water molecules at a frequency ν, and I(ν) is a transmitted light intensity at the frequency ν. Further, c is a molecular number density of the water molecules, I is a length of an optical path passing through the component to be measured, S is an absorption line intensity at the predetermined frequency ν, and K(ν) is an absorption characteristic function.
                              ln          ⁡                      (                                                            I                  0                                ⁡                                  (                  v                  )                                                            I                ⁡                                  (                  v                  )                                                      )                          =                  c          ×          l          ×          S          ×                      K            ⁡                          (              v              )                                                          (        1        )            
When the sample gas is the atmospheric pressure, the absorption characteristic function K(ν) is expressed by Formula (2) in accordance with a Lorentz profile. γL is a half width of an absorption spectrum, and decided in accordance with type, temperature and pressure of the sample gas. ν0 is a center frequency of the absorption spectrum.
                              K          ⁡                      (            v            )                          =                              γ            L                                π            ⁡                          [                                                                    (                                          v                      -                                              v                        0                                                              )                                    2                                +                                  γ                  L                  2                                            ]                                                          (        2        )            
Next Formula (3) is held from Formula (1) and Formula (2) above.
                                          ln            ⁡                          (                                                                    I                    0                                    ⁡                                      (                    v                    )                                                                    I                  ⁡                                      (                    v                    )                                                              )                                =                      c            ×            l            ×            S            ×                                          γ                L                                            π                ⁡                                  [                                                                                    (                                                  v                          -                                                      v                            0                                                                          )                                            2                                        +                                          γ                      L                      2                                                        ]                                                                    )                            (        3        )            
When a wavelength tunable laser is used, whose oscillating frequency width is far smaller than a line width of the absorption spectrum, such as a DFB (Distributed Feedback) semiconductor laser, it is possible to perform measurement at each frequency ν without separately using a spectrometer.
An absorption intensity I(ν0) at the center frequency ν0 is expressed in Formula (4) as ν=ν0 in Formula (3).
                              ln          ⁡                      (                                                            I                  0                                ⁡                                  (                  v                  )                                                            I                ⁡                                  (                                      v                    0                                    )                                                      )                          =                  c          ×          l          ×          S          ×                      1                          πγ              L                                                          (        4        )            
Meanwhile, in infrared absorption by the water molecules in an extremely low total pressure region (high vacuum region where total pressure of the component to be measured is lower than 1 [Torr]), the absorption spectrum width is as small as the order of a few percent to a few tens of percent of expansion of the foregoing Lorentz profile. In this total pressure region, the absorption characteristic width is decided mainly by the Doppler effect. The absorption characteristic function K(ν) in this case is expressed by Formula (5) (Gaussian function) below. In Formula (5), γED is one called a Doppler width, which depends on a center frequency of the absorption spectrum, a molar weight and a temperature.
                              K          ⁡                      (            v            )                          =                              1                                          γ                ED                            ⁢                              π                                              ×                      1                                          exp                ⁡                                  (                                                            v                      -                                              v                        0                                                                                    γ                      ED                                                        )                                            2                                                          (        5        )            
In this case, Formula (6) below is held from Formula (1) and Formula (5), and ν=ν0 is made to be held in Formula (6), whereby the absorption intensity I (ν0) at the center frequency ν0 can be expressed by Formula (7) below.
                              ln          ⁡                      (                                                            I                  0                                ⁡                                  (                  v                  )                                                            I                ⁡                                  (                  v                  )                                                      )                          =                  c          ×          l          ×          S          ×                      1                                          γ                ED                            ⁢                              π                                              ×                      1                                          exp                ⁡                                  (                                                            v                      -                                              v                        0                                                                                    γ                      ED                                                        )                                            2                                                          (        6        )                                          ln          ⁡                      (                                                            I                  0                                ⁡                                  (                                      v                    0                                    )                                                            I                ⁡                                  (                                      v                    0                                    )                                                      )                          =                  c          ×          l          ×          S          ×                      1                                          γ                ED                            ⁢                              π                                                                        (        7        )            
In general infrared absorption spectroscopy using laser light, the absorbed light intensities I0(ν0) and I(ν0) at the center of the absorption line are measured from Formula (4) or (7) above, to calculate an amount of the component to be measured in the sample gas.
Further, as a gas analyzing method using laser light, there is a detection method referred to as light absorption spectroscopy (hereinafter referred to as a harmonic synchronous detection method) performed by means of harmonic detection which detects second harmonic component in an absorption spectrum waveform, and the like (e.g. see U.S. Pat. No. 5,880,850 and Unexamined Japanese Patent Publication No. 2002-184767). The harmonic synchronous detection method is known especially as a high sensitive detection technique among the infrared absorption spectroscopy, and is a detection method which is effective when a light absorption amount of the component to be measured is minute.
The harmonic synchronous detection method will be described based on Reference 1. In the case of the light absorption amount of the component to be measured being minute as in the case of harmonic detection being required, Formula (1) as the Lambert-Beer Law can be approximated by the following Formula (8).
                                          ln            ⁡                          (                                                                    I                    0                                    ⁡                                      (                    v                    )                                                                    I                  ⁡                                      (                    v                    )                                                              )                                ≈                                                                      I                  0                                ⁡                                  (                  v                  )                                            -                              I                ⁡                                  (                  v                  )                                                                                    I                0                            ⁡                              (                v                )                                                    =                  c          ×          l          ×          S          ×                      K            ⁡                          (              v              )                                                          (        8        )            
Performing the harmonic detection requires modulating a frequency of light, with which the component to be measured is irradiated. When a modulation amplitude of a sine-wave signal for modulating a frequency is a and the frequency is ω, the frequency of light at time t is defined by the following Formula (9).νmod(t)=ν+a cos ωt  (9)
In second harmonic detection, a signal component corresponding to a twofold frequency 2ω is extracted by synchronous detection out of detection signals from the light receiving section. When the light absorption amount is minute, the second harmonic detection signal intensity Signal(ν) at the frequency ν has a relation as in the following Formula (10). Hence a relation of the following Formula (11) is obtained from Formula (8). In Formula (11), const is a proportional constant, and changes in accordance with sensitivities of a detector and a harmonic synchronous detection circuit. A method for deciding this proportional constant const is to previously measure a gas with a known molecular number density, such as a gas whose molecular number density has been calculated by measurement based on Formula (1) above, thereby to decide the constant
                              Signal          ⁡                      (            v            )                          ∝                  (                                                    I                0                            ⁡                              (                v                )                                      -                          I              ⁡                              (                v                )                                              )                                    (        10        )                                                      Signal            ⁡                          (              v              )                                                          I              0                        ⁡                          (              v              )                                      =                  const          ×          c          ×          l          ×          S          ×                                    ∫                              -                π                            π                        ⁢                                          K                ⁡                                  (                                      v                    +                                          a                      ⁢                                                                                          ⁢                      cos                      ⁢                                                                                          ⁢                      θ                                                        )                                            ⁢                              cos                ⁡                                  (                                      2                    ⁢                    θ                                    )                                            ⁢                                                          ⁢                              ⅆ                θ                                                                        (        11        )            
Although the harmonic synchronous detection method is highly sensitive, precise measurement is possible only on a condition where the approximation of Formula (8) above is held. Therefore, a precise detection result can be obtained when the component to be measured is one with a low molecular number density, whereas a precise detection result cannot be obtained when the component to be measured is one with a high molecular number density.
Also in the laser absorption spectroscopy, a method (hereinafter referred to as direct absorption spectrometry) for directly measuring I0(ν0) and I(ν0) and obtaining a molecular number density of a component to be measured from Formula (4) or (7) is used, for example, for measuring a sample containing moisture with a relatively high molecular number density such as a moisture molecular number density in an aerial environment, whereas the harmonic synchronous detection method is used in such an area as measurement of minute amounts of moisture molecular number densities in a particular gas for use in a semiconductor manufacturing line. Further, since detection circuits are configured in different manners in the above two measuring methods, the respective measuring devices are configured as separate ones, and no measuring device usable for the both measuring methods exists.
Therefore, a precise measurement result cannot be obtained either in a case where the molecular number density of the component to be measured abruptly decreases while measurement is performed with the device using the direct absorption spectrometry or a case where, on the contrary, the molecular number density of the component to be measured abruptly increases while measurement is performed with the measurement device using the harmonic synchronous detection method.